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1 Supplementar information for: SI for Pattern scaling using ClimGen Pattern scaling using ClimGen: monthl-resolution future climate scenarios including changes in the variabilit of precipitation Timoth J. Osborn, Craig J. Wallace, Ian C. Harris and Thomas M. Melvin Climatic Research Unit, School of Environmental Science Universit of East Anglia, Norwich, UK Corresponding author: Timoth J. Osborn, Climatic Research Unit, Universit of East Anglia, Norwich NR4 7TJ, UK, 1 st Jul 2015 S1. Climate variables and GCM model patterns in ClimGen Table S1. CMIP3 GCMs available for pattern scaling in ClimGen and the simulations used to diagnose the patterns. Ensemble size used here GCM ClimGen Identifier 20C3M A1B A2 BCCR BCM2.0 bccr_bcm CCCMA CGCM3.1 T47 cccma_cgcm CCCMA CGCM3.1 T63 cccma_cgcm31t MIROC3.2(H) ccsr_miroc32hi MIROC3.2(M) ccsr_miroc32med CNRM CM3 cnrm_cm CSIRO Mk3.0 csiro_mk CSIRO Mk3.5 csiro_mk GFDL CM2.0 gfdl_cm GFDL CM2.1 gfdl_cm GISS AOM giss_aom GISS ModelE-H giss_modeleh GISS ModelE-R giss_modeler IAP FGOALS_g1.0 iap_fgoals INM CM3.0 inm_cm IPSL CM4.0 ipsl_cm ECHAM5/MPI-OM mpi_echam MRI CGCM2.3.2a mri_cgcm232a NCAR CCSM3.0 ncar_ccsm NCAR PCM1 ncar_pcm UKMO HadCM3 ukmo_hadcm UKMO HadGEM1 ukmo_hadgem

2 Table S2. CMIP5 GCMs available for pattern scaling in ClimGen and the simulations used to diagnose the patterns. Ensemble size used here GCM ClimGen Identifier historical rcp26 rcp45 rcp60 rcp85 bcc-csm1-1 bcc_csm CanESM2 cccma_canesm CMCC-CM cmcc_cm CNRM-CM5 cnrm_cm ACCESS1-3 csibom_access CSIRO-Mk3-6-0 csiro_mk GFDL-CM3 gfdl_cm GISS-E2-H giss_e2h GISS-E2-R giss_e2r inmcm4 inm_cm IPSL-CM5A-LR ipsl_cm5alr IPSL-CM5A-MR ipsl_cm5amr FGOALS-g2 lasgce_fgoalsg HadGEM2-CC mohc_hadgem2cc HadGEM2-ES mohc_hadgem2es MPI-ESM-MR mpi_esmmr MRI-CGCM3 mri_cgcm CCSM4 ncar_ccsm CESM1-CAM5 ncar_cesm1cam NorESM1-M ncc_noresm1m MIROC5 nies_miroc Table S1 and Table S2 list the GCMs from the CMIP3 and CMIP5 archives for which climate change patterns have been diagnosed for use in pattern-scaling (the general approach to diagnosing these patterns is discussed in Section S2, while diagnosis methods are described in detail in Section S6 to support reproducibilit of this research). Both archives contain simulations from some additional GCMs that have not been analsed for use in ClimGen, but those selected provide a good coverage across these archive balancing the number of analses needed to be undertaken (and the number of analses that users of ClimGen tpicall have resources to undertake). The selection of GCMs was guided b the number of simulations across the RCP scenarios that each GCM had simulated, models with similar lineage having simulations in both CMIP3 and CMIP5, a preference to sample across the modelling groups over sampling multiple model versions from single group and a focus on climate models rather than Earth sstem models in some cases. 2

3 Table S3. Climate variables available for pattern scaling in ClimGen 1. Variable Name CMIP output variable name Unit tmp Mean temperature C tas dtr Diurnal temperature range C tasmax tasmin tmx Mean maximum temperature C tasmax tmn Mean minimum temperature C tasmin pre Total precipitation mm/month pr wet Number of wet das das/month - cld Cloud cover % clt vap Water vapour Pressure hpa Derived from huss sst Sea surface temperature C ts 1 The variable abbreviations and units are those used in the ClimGen software application. The equivalent CMIP variable names are also listed and are used in Section S6 where the diagnosis of climate change patterns from the CMIP climate model simulations is described. S2. Diagnosing normalised patterns of change Simulated patterns of climate change are illustrated in Figure S1 for different time periods within a simulation under a single scenario. The amplitude of the local temperature changes clearl grows as global warming increases (compare Figures S1a and S1b), but when divided b the global-mean temperature change from the corresponding period of the simulation, the two normalised patterns are clearl similar (compare Figures S1c and S1d). This is especiall the case over land, where ClimGen is usuall applied. There is also a close similarit between change patterns diagnosed from different simulations under different forcing scenarios: the patterns in Figure S1a-d were calculated under the SRES (Special Report on Emissions Scenarios: Nakicenovic et al. 2000) A2 scenario, whereas Figure S1f shows the normalised annual temperature change pattern from the SRES A1B scenario simulation. The patterns shown in Figures S1c, S1d and S1f, though similar, are clearl not identical. This does not, in itself, invalidate the assumption that the pattern is invariant because the climate change signal will be contaminated b the noise of unforced variabilit simulated b the GCM. The signal-tonoise ratio can be strengthened b pooling data from multiple simulations (e.g., Figure S1e obtained b pooling data from both A2 and A1B simulations for this GCM; the correlation between this joint A2 and A1B pattern and the pattern diagnosed from onl A1B, Figure S1f, is 0.99). Mitchell (2003) made a number of recommendations about how best to diagnose the normalised change patterns to strengthen the signal-to-noise ratio (and thereb obtain a more accurate estimate of a GCM s real climate change pattern) and to improve the applicabilit of the patterns from one scenario to another. These are particularl important for variables such as precipitation, for which the climate change signal does not, in man region overwhelm the inherent, unforced climate variabilit (Hawkins and Sutton 2009). Rather than obtaining the patterns b calculating the change between two periods (tpicall the late 21 st centur minus the late 20 th centur, as was done in Figure S1b), and dividing b the corresponding ΔT (Figure S1d), we instead regress the local change against ΔT using data from the full simulation. Running means (tpicall of 30 ears) of the simulated changes are 3

4 used otherwise the regression might be dominated b the signal of interannual variabilit (e.g. the El Nino Southern Oscillation) rather than the climate change signal that is required. Such a regression uses data throughout the 21 st centur to obtain a more accurate estimate of the pattern than simpl using the final 30 ears of data (which could, b chance, be somewhat warmer, cooler, wetter or drier than the underling climate due inherent climate variabilit). Further, where an initial-condition ensemble of simulations under the same scenario is available for a particular GCM, the ensemble data are averaged together to reduce the influence of the unforced climate variabilit (which will be uncorrelated between ensemble members and the standard deviation of the variabilit will therefore decrease inversel proportional to the square root of the ensemble size). If simulations under multiple scenarios are available, then these data are pooled together and a single regression is performed (though separate regression can be applied to each scenario to assess the similarit of the patterns obtained see section 3 of the main paper). The ensemble sizes used to diagnose normalised patterns of change from the CMIP3 and CMIP5 GCM for use in ClimGen, are listed in Tables S1 and S2, respectivel. These regressions are performed separatel for each grid cell on the GCM s original grid, for each of the 12 calendar months (to capture the annual ccle in the climate change signal), and for each of the climate variables listed in Table S3. The slope of the regression line at each grid cell gives the normalised climate change pattern (e.g., Figure S1e). For climate variables where the climate change signal is weaker, the patterns contain noticeable localised variance associated with inaccuracies arising from the inherent, unforced variabilit in the GCM simulation. This is reduced b replacing each monthl slope b a average of the precedin current and subsequent monthl slopes for these variables (cloud cover, diurnal temperature range and the gamma shape parameter of precipitation). The intercept of the regression line can be inspected to identif regions where the assumption of linearit ma be invalid: if the relationship is linear then it should pass close to the origin (since if there is no global warmin ΔT = 0, we expect no change in the local climate). A complete mathematical description of the diagnosis of the normalised climate change patterns used in ClimGen is provided in section S6. To facilitate comparison of different GCMs and the combination of climate change with the observed climatolog, the normalised climate change patterns are interpolated to a 0.5 longitude b 0.5 latitude grid. This is a finer resolution grid than an of the GCMs currentl used in ClimGen, but it should not be confused with statistical downscaling. It is interpolation, rather than downscalin because the climate change patterns on the finer grid still closel resemble the patterns on the coarser GCM grid there is no finer-scale information (with one exception) derived from empirical analsi as would be the case with downscaling (Maraun et al. 2010). The exception is that finer-scale information associated with the land-sea boundar is utilised during the interpolation (Figure S2). Grid cells on the finer grid that are classified as land are interpolated giving greater weight to the values from GCM grid cells that are classified in the GCM as land, and vice versa. This requires the land-sea mask for each GCM. If there is no obvious land-sea difference in the simulated climate change pattern, then it makes no difference to the result. However, in some cases (e.g. summer temperature change in regions where the soils dr out, with a resultant amplification in warming over land) this innovation can make a significant difference near to coast even where some land areas or coastlines are not well resolved on the GCM grid (such as Ital and other Mediterranean and Black Sea coasts: compare Figure S2b and c). 4

5 Figure S1. Annual temperature changes simulated b UKMO HadCM3. Changes under the SRES A2 scenario for (a,c) the 2040s and (b,d) the 2080 both relative to the mean: (a,b) absolute temperature changes ( C); (c,d) temperature changes divided b their global-mean (1.5 C for the 2040s and 3.3 C for the 2080s). Normalised patterns of annual temperature change ( C/ C) obtained b regression of UKMO HadCM3 data pooled from simulations under (e) SRES A2 and A1B scenarios; and (f) SRES A1B scenario onl. 5

6 Figure S2. Illustrating the interpolation with differential weighting of land and ocean model grid cells. (a) Normalised pattern of Jul temperature change ( C/ C) from the CSIRO-Mk3.6.0 GCM on the original model grid. (b) Equall-weighted interpolation to the 0.5 resolution grid. (c) Interpolation to the 0.5 resolution grid with higher weighting given to values from grid cells classed as land (ocean) in the GCM when estimating values for 0.5 grid cells that are over land (ocean). 6

7 S3. Separating the effects of climate change and unforced variabilit The approaches developed and reported in this paper allow the generation of climate projections that combine a climate change signal (from pattern scaling 1 ) with unforced variabilit (from detrended observation but with changes in variabilit obtained through pattern-scaled climate changes to the distribution shape). This is required for analsis that depends on both climate change and variabilit, and that needs a sizeable sample of data to capture the variabilit, such as drought frequenc analsis. However, combining climate change with unforced variabilit can then obscure the climate change signal if a single realisation is used. When using ClimGen projections as input to climate impact model the effects of variabilit and climate change can be separated b generating ensembles of projections with the same climate change signal but different samples of unforced variabilit. This is similar to using GCM initial condition ensemble though here we are limited b the length of the observational record from which samples of observed anomalies are taken (the reliable record is limited to in man parts of the world) and thus the full range of variabilit ma not be sampled. Two approaches have been implemented to achieve thi illustrated in Figure S3. First, a number of sequences can be generated (Figure S3a), each for a fixed, but different, globalmean temperature rise (e.g. sequences of, sa, 30 or 50 ears with constant T! and ear-to-ear variations arise onl from V t! ). If the observed anomalies used are the same for each sequence (including for T! = 0 to represent the reference climate for ), then the onl difference between each sequence is the climate change (determined b the prescribed T! ). Arnell et al. (2014) used this approach to determine climate change impacts as a function of global temperature. For drought frequenc analsi the return period will change fairl smoothl as the global-mean temperature is graduall increased because the same 50-ear sample of data can be used for each sequence but with graduall increasing modification of the values in the sample. A second approach is necessar where the impact depends on the transient change in climate (perhaps because the rate of change is important, such as the gradual response of vegetation or soil carbon; Gottschalk et al., 2012) and so a 50-ear sequence under a fixed temperature increase is not appropriate. A sequence of 140 ears (from 1961 to 2100) can be generated with a graduall increasing T! (representing the global response under some particular scenario) and a given segment of observed anomalies can be repeated throughout the climate projection. This is another reason wh detrended anomalies are used, otherwise the repeated segments would form a saw tooth shape in the presence of a trend in each segment. An ensemble of such projections can be generated, each with the phase of the observed anomalies shifted sstematicall in time (Figure S3b). When using a 30-ear segment of observed anomalies to represent the variabilit, up to 30 projections could be generated (each with the observed anomalies shifted b 1-ear steps). If the climate impact model is driven b each ensemble member in turn, and then the results averaged, this will ield a timeseries of the response to onl climate change, since ever ear will be averaged across the full set of observed anomalies within the ensemble. If the impact is evaluated in N-ear period a smaller ensemble of projections (with observed anomalies shifted b N-ear steps) will be sufficient, such as Figure 3 in the main paper which used this approach to evaluate the frequenc of dr months in 10-ear windows. That example (expanded on in Section S4 for different thresholds to define dr months) illustrates the value of this approach: the ensemble mean of 5 projections analsed in a 10-ear running window closel replicates the frequenc of dr months found using a 50-ear running window, but extends the results to 2095 (the centre of the final 10-ear window) compared with 2075 for the 50-ear window. 1 Note that, despite pooling multiple RCP simulations and multiple initial condition ensemble members (where available), the diagnosed patterns will still be partl contaminated b the remaining unforced variabilit in the average of this pooled data. This contamination is not considered here. 7

8 The ensemble spread indicates both the range of unforced variabilit (though this is less than that simulated b the GCM, possibl because the ClimGen ensemble is based on onl a 50-ear sample of variabilit) and the potential inaccurac of the results if the had been based on onl a single projection. (a) (b) Figure S3. Illustration of two approaches to generate projections that allow the climate change signal to be separated from the influence of the superimposed variabilit. The data shown here are dumm data, generated for illustrative purposes onl and differ between the panels. (a) The generation of multiple 50-ear sequences of monthl local precipitation (right-hand axi expressed as anomalies), each representing the climate for a specified amount of global-warming (left-hand axis). Pattern-scaling assumes that the local change is a function (here a linear function) of ΔT, with coefficient estimated from a GCM simulation. Each sequence is not necessaril associated with a particular ear, though in this example the are positioned on the x-axis according to an arbitrar scenario of temperature rise. (b) Six sequences (in colour, each offset b 60 mm/month for displa purposes) of monthl local precipitation under the same transient scenario (note the downward trend in each case) appended to the observed record for this grid cell (black). The section (light gre shading) of the observed record is repeated multiple times through the projection, but in each case it begins 5 ears earlier. Therefore pooling output for a 5-ear period (e.g , also shaded) from six transient impact simulations driven b these six sequences will sample anomalies from all 30 ears and the onl difference between this 6 5 sample and the reference period arises because of the climate change signal in the scenario. 8

9 S4. Projections of dr-month frequenc with fixed and changing distribution shape In the main text, changes in the frequenc of ver dr August months across Europe under the RCP8.5 scenario were used to illustrate (Figure 3) the importance of changes in variabilit as well as changes in mean climate. Pattern-scaled changes were obtained b scaling patterns of changes in mean and gamma shape parameter from the MPI-ESM-MR GCM b the global temperature changes simulated b that model under the RCP8.5 scenario. In ClimGen, changes in the shape of the precipitation distribution (modelled as a gamma distribution, hence the gamma shape parameter is considered) are diagnosed from GCM simulations and then projected using the same pattern-scaling technique as used for changes in mean precipitation. These are then used to perturb the timeseries of precipitation anomalies (derived from the observational record) prior to combining it with the projections of future mean precipitation. Compared with projections where onl the mean precipitation is allowed to var, those that also include changes in precipitation variabilit exhibit a greater increase in the occurrence of ver dr months (below the th percentile value in Figure 3 of the main text) that much more closel emulates the increased frequenc diagnosed directl from the GCM simulation (in this example, the MPI-ESM-MR GCM). Similar results are shown in the following supplementar figures but for different percentiles to define dr months (Figures S4 7 for the 4th, 8th, 12th and 20th percentile respectivel). These percentiles were chosen as multiples of 2 percentiles because, with a sample size of 50 value this avoids biases in frequenc timeseries during the reference period (Zhang et al., 2005). Even out to the 20th percentile, changes in precipitation variabilit increase the occurrence of dr month though b a graduall diminishing amount consistent with Figure 1b of the main text. Note that this example (dr European summer months) was selected because, b inspection of the change patterns for precipitation gamma shape, we expected the change in variabilit to be important. There will be other regions where the effect is less marked. Figure S4 (next page). RCP8.5 projected changes in dr August months with and without changes in precipitation variabilit and compared with direct GCM results. Fraction of August months during that are dr in projections from (a) ClimGen changing onl the mean precipitation; (b) ClimGen changing both the mean precipitation and the distribution shape of the precipitation anomalies; and (c) direct GCM output. The GCM used here (for ClimGen change patterns and direct GCM output) is MPI-ESM-MR and dr months are defined as precipitation below the reference period ( ) 4th percentile for the ClimGen or GCM data. B definition, the frequenc of such values is 0.04 during the period and therefore frequencies during the period below 0.04 represent fewer dr August month while values above 0.04 indicate more frequent dr months. White areas are where there were too man months with zero precipitation during the reference period to define the 4th percentile. (d) Timeseries of the fraction of dr months averaged over the region defined b the black rectangle in the other panels for 10-ear (thin lines) and 50-ear (thick lines) running window plotted against the central ear of each window. Blue: GCM; red: ClimGen mean changes onl; black: ClimGen mean and variabilit changes. Onl one simulation is available for the GCM, whereas for ClimGen the 10-ear running window results are based on an ensemble of 5 projections for appended to the CRU TS observations and the mean of this ensemble is shown for both cases (thin lines) and the ±2 standard deviation range around the ensemble mean is shown for the case with changes in both mean and variabilit (gre shading). 9

10 10 SI for Pattern scaling using ClimGen

11 Figure S5. As Figure S4, but for the 8th percentile. 11

12 Figure S6. As Figure S4, but for the 12th percentile. 12

13 Figure S7. As Figure S4, but for the 20th percentile. 13

14 S5. Multi-model mean climate change patterns The diagnosis of normalised patterns of change and their interpolation to a common grid enables straightforward comparison of the climate changes simulated b different multi-model archives of simulation even though the scenarios used ma have been different (e.g. SRES scenarios for CMIP3 and RCP scenarios for CMIP5). Figure S8 demonstrates close agreement between CMIP3 and CMIP5 annual temperature changes at the largest scales over land, with greatest warming at high northern latitudes as well as in some subtropical regions where local warming is about 1.5 times the globalmean warming. Reduced warming around man coasts and, with the exception of South America, in the equatorial band is apparent (note that surface air temperature warms more over land than over the oceans in these model so the global mean of these land-onl normalised changes is greater than one). The difference between the multi-model means (Figure S8c) reveals enhanced relative warming at man mid-to-high northern latitudes in CMIP5 compared with CMIP3 (a value of 0.2 indicates warming is greater b an additional 20% of the global-mean warming). Note that these changes are relative to the global-mean, and do not indicate the absolute differences in warming between the two ensembles. The global land mean of the CMIP5 minus CMIP3 differences is slightl positive (0.04 C/ C) indicating an enhanced increase in land-sea contrast in CMIP5 compared with CMIP3. For the percentage change in annual precipitation, the overall patterns of wetting over mid-to-high northern latitude much of eastern and southern Asia, northern tropical Africa and parts of South America, and dring in the Mediterranean, Caribbean, Central America and southwest Africa are similar in both CMIP3 and CMIP5 (Figure S8d,e). The differences (Figure S8f) show that the wetting in high northern latitudes is slightl less in CMIP5, but the CMIP5 ensemble is wetter than CMIP3 over much of the northern tropics and out towards the northern mid-latitudes. That i the dring in the Mediterranean is less pronounced in CMIP5, while the wetting in eastern and southern Asia, the Arabian Peninsula and the Horn of Africa is enhanced. The global land mean of the CMIP5 minus CMIP3 differences is positive (1.3%/ C) indicating a significant additional overall increase in land precipitation for CMIP5. There is considerable inter-model spread in these multi-model ensembles which is not shown here but which ClimGen was developed to explore (see Section 4c of the main paper for an example). 14

15 SI for Pattern scaling using ClimGen Figure S8. Comparing the CMIP3 and CMIP5 multi-model-mean normalised changes. Multimodel-mean normalised changes and differences for (a) CMIP3, (b) CMIP5, and (c) CMIP5 minus CMIP3 annual temperatures; and (d) CMIP3, (e) CMIP5, and (f) CMIP5 minus CMIP3 annual precipitation. Units are C/ C for temperature and %/ C for precipitation. White areas in ver dr regions in panels (e) and (f) are where the relative change in precipitation was not calculated for CMIP5 models if the present-da simulated precipitation was almost zero. 15

16 S6. Diagnosing climate change patterns for use in ClimGen Introduction 1. A complete mathematical description of the diagnosis of normalised climate change patterns from the CMIP3 multi-model ensembles is provided here. These calculations were used to generate the climate change patterns used in the ClimGen climate generator software from the CMIP3 data base of atmosphere/ocean General Circulation Models (GCMs) that were used extensivel in the Fourth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC), published in These methods were also used for the QUMP and CMIP5 ensemble with minor modifications according the availabilit of different scenario simulations and climate variables. Indeed, these methods can be applied to the output from an appropriate GCM simulations. To provide the most precise description of the method the CMIP climate variable names have been used in this section because the are the data that were used in the calculations. Refer to Tables S1, S2 and S3 for the correspondence between CMIP and ClimGen models names and variable names. Model names used in ClimGen are limited in length b the ClimGen file naming convention, so the are constructed b joining the modelling group name and the GCM name, but with each component shortened b removing punctuation such as dashes and full stops. Input data 2. For each GCM (g), that has been run for each scenario (s), possibl for an ensemble of individual runs (e), we have output for a range of variables (v) at each GCM grid box (i), for each month of the ear (m) and for a time series of ears (). This data set is denoted b ı X e,,v 3. For the CMIP3 data base, we have around 20 GCM and we use data from 3 scenarios: s = 0 denotes the 20c3m run with historical forcing s = 1 denotes the sresa1b run with SRES A1B forcing s = 2 denotes the sresa2 run with SRES A2 forcing Note that there are other forced runs available (e.g., under SRES B1 forcing) but diagnosing climate change patterns is less accurate from weaker-forcing scenarios because the signal-to-noise ratio is weaker. There are also control simulations available, which might be used to identif and remove an model trends that are unrelated to the forcings (i.e., model drift due to initial conditions being different to a model s preferred stead state), but these were not used in the current version of the process. Global-mean temperatures 4. We calculate global-mean temperatures from the grid-box near-surface monthl-mean air temperature data (v = tas), taking into account the converging model grid b weighting b the cosine of the latitude of the centre of each grid box, and taking into account variable latitudinal spacing of grid boxes (some models use equal spacin but not all do) b weighting b the latitudinal span of each grid-box row [either calculated from the lat_bnds values available in the netcdf model data file or estimated b 0.5 (lat row+1 lat row 1 ) for latitude row except just (lat row+1 lat row ) for the first row or (lat row lat row 1 ) for the last row]. We then calculate the annual-means of these global-mean temperature and denote them b T e, (here s = 0, 1, 2) 16

17 5. Average across all ensemble members (NE v ) that are available for this particular GCM, scenario and variable v = tas ı T = j= NE v T e= j, j=1 NE v 6. We now append T ı for the period from 20c3m to the beginning of both T ı sresa1b and sresa2 scenario which usuall each cover the period If ever GCM being analsed runs through to at least 2100, then use 2100 instead of 2099 as the final ear. Do not use an data beond 2100 even if available. Also note that for some GCM the 20c3m run extends to 2000, 2001 or even 2002, while the scenario runs begin the ear immediatel following the end of the 20c3m run. In these case use the 20c3m run until its final ear, and append the scenario data immediatel after that. This should give a continuous time series of annual- and global-mean temperature for each scenario, running from , although the will all be identical for (or whenever 20c3m finishes) c3m sresa1b 20c3m sresa2 7. Denote these combined series b T (now s = 1, 2 since s = 0 has been appended to the start of each scenario) 8. Convert each series to anomalies b subtracting their own mean j=1990 T = j j=1961 T s = 30 (in fact, for each GCM, the mean will be the same across all scenarios because it comes from the common 20c3m data) from ever ear ΔT = T T s and store these global-mean temperature anomal time series for later use. 9. For a given running window length W (tpicall either W = 30 or W = 49), calculate running means of the global-mean temperature anomal time series ΔT = j= +W 1 ΔT = j j= W (now = W+1) 17

18 10. If W = 49, then re-anomalise the running mean time series b subtracting the mean (which will have alread been calculated as the first running mean value) i.e., replace ΔT b ΔT ΔT =1951 if W = 49 It is not necessar to do this for W = 30, because in that case we want anomalies from the mean, and we alread had this before computing the running mean so the running means should still have a value of zero when = Store these running mean global-mean temperature anomalies for both W = 30 and W = 49 for later use. Individual grid-box variables 12. A similar process is carried out for the individual variables at the individual model grid boxes as was done with the global-mean temperature, except that we do not (et) average across the ensemble which adds a complication when the number of members in each scenario s ensemble is different (discussed later). 13. Since the following calculations are done entirel separatel for each grid box, variable and month of the ear, we simplif this notation b replacing X ı e,,v with X ı e, though we re-introduce v in some place where it is necessar to indicate that the values depend on which variable is being considered. 18

19 14. We now append X ı for the period from 20c3m to the beginning of both X ı sresa1b and X ı sresa2 scenario which usuall each cover the period Follow step 6 for when the runs cover slightl different periods than this. The onl difference is that step 6 was dealing with ensemble mean whereas here we still have individual ensemble members. A complication arises when the number of ensemble members is different for the 20c3m (NE g, s=0, v ), sresa1b (NE g, s=1, v ) and sresa2 (NE g, s=2, v ) scenarios. For each future scenario case (s = 1, 2), create max{ NE g, s=0, v, NE g, s, v } time series and fill them according to the example that follows: If NE g, 0, v = 8, NE g, 1, v = 7, and NE g, 2, v = 5 (which is the case for v = tas for g = ncar_ccsm3_0), create the combined time series indicated below. If the number of ensemble members for 20c3m is less than the number for either one or both of the future scenario then some of the combined time series would have missing values in the section and not in the section c3m run 1 sresa1b run 1 20c3m run 2 sresa1b run 2 20c3m run 3 sresa1b run 3 20c3m run 4 sresa1b run 4 20c3m run 5 sresa1b run 5 20c3m run 6 sresa1b run 6 20c3m run 7 sresa1b run 7 20c3m run 8 missing values c3m run 1 sresa2 run 1 20c3m run 2 sresa2 run 2 20c3m run 3 sresa2 run 3 20c3m run 4 sresa2 run 4 20c3m run 5 sresa2 run 5 20c3m run 6 missing values 20c3m run 7 missing values 20c3m run 8 missing values 15. Denote these combined series of raw values b X e, (now s = 1, 2 since s = 0 has been appended to the start of each scenario) 16. For each ensemble member of each scenario and GCM, compute a time series of low-frequenc variations b appling a 30-ear Gaussian-weighted low-pass filter to the raw values X e, to obtain ) X e, Note that we alwas use a 30-ear filter, regardless of the size of our running window (W) used elsewhere in this analsis. Further, note that the 30-ear Gaussian-weighted filter pads the ends of the time series X so that the filtered series ) X extends to the ends of X. 19

20 17. For each ensemble member of each scenario and GCM, compute a time series of high-frequenc deviations from the low-frequenc series X e, ʹ = X e, X ) e, and a time series of high-frequenc fractional deviations X e, ʹ ʹ = X e, ) X e, 18. For the same running window length as in step 9, W, extract the set of raw values that fall within a window beginning in ear and running through to ear +W 1, keeping ensemble members separate still, so that our set is denoted b X e,... +W Now consider the same window of data for all ensemble members of the current scenario, but discard an entire window of data for an ensemble member if an of the raw values in this window are missing. For those ensemble-member sets that remain, pool all the sets of raw values together (i.e., combine into a bigger, single set of values whose order is not important). The size of each pool of raw values will change as the running window slides along if the number of ensemble members is different between 20c3m and sresa1b, or between 20c3m and sresa2. As the running window hits the 1999/2000 transition, an missing values (see example in step 14) will trigger the condition described at the start of this step: as soon as an value in the running window is missin all values for that ensemble member will be removed from the current running window. In the pool of remaining value we have values from ears to +W 1 and from all ensemble members that have not been discarded. The size of this pool of values (NP,v ) is the product of W and the number of non-discarded ensemble members. We assign this pool of raw values to ear at the start of the running window, denoting the pool b X,pool (pool = 1 NP,v ) 20. Repeat steps 18 and 19 twice more to produce pools of the deviations and pools of the fractional deviations (from step 17) ʹ X,pool ʹ ʹ X,pool giving us three pools (raw value deviation and fractional deviations) of values for each running window. Temperature variables 21. All calculations and output files for temperature variables should use units of Kelvin (K); the slope coefficients will therefore be in units of K/K. The temperature variables considered are the mean, minimum and maximum near-surface air temperatures (ta tasmin and tasmax), the diurnal temperature range (dtr) derived as tasmax tasmin, and the skin (i.e., surface) temperature (ts). Results from those CMIP3 models with tasmin and tasmax data available, confirmed that, as expected b definition, the dtr change patterns are almost inseparable from the difference between the tasmax and tasmin patterns. The tas patterns are also ver 20

21 similar to the mean of the tasmax and tasmin patterns and it is sufficient, therefore, to diagnose onl the tas and dtr pattern because the tasmax and tasmin patterns can be calculated later from (tas dtr) and (tas 0.5 dtr). There is an additional important step for the ts variable. For ClimGen, we actuall want sea surface temperatures (SST). Although this is available as an ocean variable (tos) for most models in CMIP3, some GCMs have ocean and atmosphere models that operate on different grids and thus tos will be on a different grid to the other variables used in ClimGen. We ma consider using tos in a future version, but currentl we instead use the ts variable, which is available on the same (atmosphere model) grid as the other variables. The ts variable is the skin temperature of whatever surface is present, whether land, ice or sea, or an average if more than one surface tpe is present in a model grid box. If an ocean region is (at least initiall) covered partl or full with sea ice, which can allow ver cold t then ts warming can appear to be ver large even though SST ma hardl change. To make the ts change patterns more closel related to the SST change pattern all values ts < K (i.e., < 1.8 C, the approximate freezing point of sea water) must be set to K (or 1.8 C if data are in those units) before an analsis is begun. For all temperature variables (v = ta dtr, ts) we use W = 30 to generate these running window pools. We then simpl take the mean of all the raw values in each running window pool, assigning each mean value to the ear at the start of the running window X = NP,v X,pool= j j=1 NP,v 22. And then we express the time series of running pool means as changes from the reference period ΔX = X X = Finall, we calculate the simple linear (i.e., least-squares) regression of ΔX (on the -axis ) against ΔT (from step 9 or 10, on the x-axis ), using all ears and both scenarios s together. The regression gives us the intercept a v and slope b v ΔX,v a v + b v ΔT and these are calculated and stored for ever GCM, month of the ear, grid box and variable. 24. The slope values define our pattern of change per unit degree of global warming for each GCM, month, grid box and temperature variable. This pattern is used for additive pattern scaling (eq. 2 of the main paper). Ideall the intercept values should all be zero, since for no change in globalmean temperature we expect no climate change in an variable. We do not, however, force the intercept to be zero b fitting the line = bx because the regression ma implicitl provide a better estimate of the reference period mean than the actual reference period mean (since the simulated values during the reference period will include random internall-generated variabilit, just like an other period). Nevertheles we expect that the intercept values should be quite close to zero, and the are stored so that the cases that result in the largest (absolute) values can be inspected to rule out an particular problems. Scatter plots of the ΔX and ΔT value together with the best-fit regression line (computed in step 23), are also useful to identif potential problems. 21

22 Precipitation 25. All calculations and output files for precipitation should use units of mm da -1 ; the slope coefficients of the absolute changes will therefore be in units of mm da -1 K -1. Most GCM files use kg m -2 s -1, and need to be converted to mm da -1 b multipling b s da -1 (because 1 kg m -2 is equal to 1 mm when the densit of water is 1000 kg m -3 ). For precipitation, we are interested in changes in both the mean precipitation and its inter-annual variabilit. These are diagnosed separatel Mean Precipitation 26. The procedure is ver similar to that for the temperature variables (i.e., steps 21 to 24) except that we additionall diagnose relative changes (similar, but not identical, to percentage changes) as well as absolute change and we fit both linear and exponential curves to the relative changes. Thus we have three sets of output: linear fit coefficients for the absolute change linear fit coefficients for the relative change and exponential fit coefficients for the relative changes. 27. For the precipitation variable (v = pr) we again use W = 30 when considering changes in the mean precipitation, to generate the running window pools. We then simpl take the mean of all the raw values in each running window pool, assigning each mean value to the ear at the start of the running window X = NP g,, v j= 1 X NP, pool= j, v 28. And then we express the time series of running pool means as absolute changes from the reference period ΔX = X X = And also as relative changes from the reference period δ X = X X = 1961 Note that we could have called these fractional changes rather than relative change but we are alread using fractional deviations to describe the high-frequenc deviations calculated in step 17 and so to describe these running pool means as fractional changes might lead to confusion. 22

23 30. We calculate the simple linear (i.e., least-squares) regression of both the absolute change Δ X g, s,, and separatel of the relative change δ X g, s,, against Δ T g, s, (from step 9 or 10), using all ears and both scenarios s together. This gives us intercepts and slopes so that Δ X, v a v + b vδtg, and δ X, v c v + d vδtg, 31. For an grid box and month when the reference period mean is exactl zero, X = 1961 = 0, the relative changes will all be undefined (division b zero) and in these cases the intercept, c, and slope, d, are set to some appropriate missing value code. 32. The note in step 24 about the intercept applies here too. We expect the straight line fit to pass close to (0,0) for the absolute change and close to (0,1) for the relative change but we do not constrain it to do this in either case. It is (0,1) for the relative change because a value of 1 indicates that the precipitation is equal to the reference precipitation and thus there is no climate change. 33. For the relative change we also fit an exponential curve that is constrained to pass through (0,1) δ X, v e f ΔT g, v g, To determine the slope coefficient, f v, we first replace an values of δ X < 0.01 b 0.01 because the logarithm of zero is undefined, and then we take the natural logarithm of the δ X values and regress these against the Δ T values as before. After taking logarithm our previous equation becomes a straight line passing through (0,0) [which is (0,1) in original unit because ln 1 = 0] lnδ X, v f vδtg, and we obtain the values of f v using ( lnδx, v)( ΔTg, ) s ( ΔTg, ) f = sumover all and all v 2 sumover all and all s which is the standard formula for estimating the least-squares linear fit constrained to pass through the origin [i.e., slope = Σ( i x i ) / Σ(x i 2 )]. 34. The regression intercept a and c, and the regression slope b, d and f, are calculated and stored for ever GCM, month of the ear and grid box. The b pattern of slopes is used for additive pattern scaling (equation 2 of the main paper); the d pattern of slopes is used for multiplicative pattern scaling (equation 3 of the main paper); the f pattern of slopes is used for multiplicative pattern scaling as an exponential function of global temperature (equation 4 of the main paper). 23

24 Interannual Variabilit of Monthl Precipitation 35. The procedure is similar in some was to that used to diagnose the changes in mean precipitation simulated b each GCM. The main exceptions are that we use the fractional deviations defined in step 17, we pool them (see steps 18,19 and 20) using the longer W = 49 window length, and rather than averaging all values in each pool (step 27) we instead fit a gamma distribution to them and subsequentl utilise the fitted gamma shape parameter in the remaining procedure. 36. Take the time series of high-frequenc fractional deviations of precipitation (v = pr) for each ensemble member of a scenario, extract the set of values that fall within a window beginning in ear and running through to ear +W-1, with window length W = 49: ʹ ʹ X e,... +W Now pool across all ensemble members available for this scenario, following the procedure described in step 19 (in fact, step 20 had alread described this for the high-frequenc fractional deviations): ʹ ʹ X,pool 38. The high-frequenc fractional deviations were calculated b dividing each value b the lowfrequenc smoothed series. If this low-frequenc smoothed series is zero (which can occur in desert areas), then the high-frequenc fractional deviation will be undefined. Remove such values from the pool. Count how man of the remaining values are zero and how man are non-zero (positive; b definition there should be no negative values). If there are less than 10 remaining non-zero values in the pool, or if there are more zeros than non-zeros in the remaining value then set the gamma shape parameter to undefined for this pool and move on to the next window (i.e., shifted forward b one ear). 39. The gamma distribution is not defined for zero values. If we have reached this step, then we have at least 10 non-zero values and no more than half of the values are zero. If there are an zero then find the smallest of the non-zero values (X min ) and replace each zero value with 0.5X min. 40. For this pool of value calculate the best-fit gamma shape parameter b using the Thom (1958) approximation to the maximum-likelihood method (see Wilk 1995). First calculate Thom s d value, as the natural logarithm of the mean of the value minus the mean of the natural logarithms of the values: d = ln NP,v ʹ ʹ X,pool= j j=1 NP,v NP,v j=1 ( lnx,pool= ʹ ʹ j ) NP,v X ʹ ʹ has been modified according to the previous two step removing undefined values Note that and replacing zeros with 0.5X min, and that the size of the pool, NP, also needs to be reduced b the number of undefined values that were removed. If d = 0 (because all values are identical), then set the gamma shape parameter to undefined for this pool and move on to the next window. 24

25 41. Calculate the gamma shape parameter (note that the shape parameter is dimensionless and should alwas be > 0) using: d α = 3 4d 42. Repeat this process to obtain a value of the gamma shape parameter for each running window pool for this GCM, grid box, month of the ear and scenario. Then calculate relative changes in the shape parameter from the reference period shape parameter: δα = α α =1951 Note that we onl work with relative changes for the gamma shape parameter, never with absolute changes. For an grid box and month for which the reference period shape parameter is undefined, then all the relative changes will also be undefined, and in these case the regression intercepts and slopes are set to some appropriate missing code. 43. Following a similar procedure to step 30, we calculate the simple linear (i.e., least-squares) regression of the relative changes in shape, δα, against ΔT (from step 10), using all ears and both scenarios s together. Note that the ΔT values are now the global-mean temperatures calculated from the W = 49 ear running window, referenced to the 49-ear mean. δα,v c v + d v ΔT 44. We also fit an exponential curve, constrained to pass through (0,1), to the relative changes in shape, using the same formula as shown in step 33, ielding the regression slope f v. 45. The regression intercept c, and the regression slope d and f, are calculated and stored for ever GCM, month of the ear and grid box. Cloud cover 46. Patterns of cloud cover change are diagnosed from the CMIP3 model output variable clt (cloud area fraction). CMIP3 documentation indicates that this variable is stored in % unit but this was checked for each model in case the stored it as a faction. When reading clt data, divide b 100 to convert it from % to fraction and do all the diagnosis in terms of fractional cloud cover. 47. The procedure is ver similar to that for the temperature variables (i.e., steps 21 to 24) except that we additionall use logistic regression. We do not consider relative change onl absolute changes. Thus we have two sets of output: linear regression coefficients for the absolute changes and for the logistic changes in cloud cover. 25

26 48. For the cloud cover variable (v = clt) we use W = 30 for the window size, to generate the running window pools. We then simpl take the mean of all the raw values in each running window pool, assigning each mean value to the ear at the start of the running window X = NP g, s,, v j= 1 X NP, pool= j, v 49. And then we express the time series of running pool means as absolute changes from the reference period ΔX = X X = Calculate the simple linear regression of the absolute changes Δ X g, s, against Δ T g, s, (from step 9) using all ears and both scenarios s together. This gives us intercepts and slopes so that Δ X, v a v + b vδtg, 51. We then go back to the output of step 48, the mean of each running window pool. Limit all values to lie between and (i.e., an values below are set to 0.001, and an above are set to 0.999). This is because logistic regression does not work with either zero cloud cover or complete cloud cover. Once these limits have been applied, calculate the inverse logistic function for each value (i.e., for the mean of each running window pool) L X = ln 1 X (note that ln is the natural logarithm). 52. And then express the time series of inverse logistic values as absolute changes from the inverse logistic value that was obtained for the window pool ΔL = L L = Calculate the simple linear regression of the absolute changes in the inverse logistic values Δ L g, s, against T g, s, and slopes so that Δ using all ears and both scenarios s together. This gives us intercepts Δ L, v c v + d vδtg, 54. The regression intercept a and c, and the regression slope b and d, are calculated and stored for ever GCM, month of the ear and grid box. 26

27 Water vapour pressure 55. Vapour pressure is not available directl from the CMIP3 data base, and rarel is it available from GCMs. In most case either specific or relative humidit is available instead. Specific humidit is preferable, since the conversion from relative humidit to vapour pressure is more approximate, depending on temperature and giving potentiall incorrect values if calculated from monthl rather than dail (or hourl) data. Nevertheles since we are more interested in change patterns rather than absolute value use of vapour pressure estimated from relative humidit would still be worthwhile if that is the onl humidit variable available. 56. Some CMIP3 models provide monthl-mean near-surface specific humidit (huss). For these model the conversion to vapour pressure (from Mitchell et al., 2004; but compatible with other e.g., Willett et al., 2008) is e = qp 0.62 where e is vapour pressure in hpa, q is specific humidit in kg/k and p is atmospheric pressure in hpa (note that Mitchell et al., 2004, use atmospheric pressure at sea level). 57. For these CMIP3 model therefore, we combine huss (alread in kg/kg) and psl (converted from Pa to hpa) using the formula in step 56 to obtain vapour pressure in hpa. 58. For CMIP3 models without near-surface specific humidit (huss), monthl-mean specific humidit on the 1000 hpa pressure level was used, extracted from the specific humidit that is provided on man pressure levels (hus). The 1000 hpa hus is converted to vapour pressure using the formula in step 56, but with p = 1000 hpa. Although vapour pressure at 1000 hpa will be different in absolute terms from vapour pressure at the surface, it is likel that the pattern of changes under greenhouse-gas-induced climate change will be ver similar. 59. Having calculated vapour pressure at either the surface or at 1000 hpa, the calculation follows the same procedure as for the temperature variables in steps 21 to 24. Data are windowed with W = 30, then pooled within each window and across ensemble member the mean is taken of each pool, the running pool means are converted to anomalies b subtracting the pool mean, and finall simple linear regression of these vapour pressure anomalies against the corresponding global-mean temperature changes (using all ears and both scenarios) is applied. 60. The regression intercept a, and regression slope b, are calculated and stored for ever GCM, month of the ear and grid box. 27